Quantum algorithmic measurement

Dorit Aharonov

doi:10.1038/s41467-021-27922-0

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Quantum algorithmic measurement

2022-02-16

Dorit Aharonov

Jordan Cotler *

Xiao-Liang Qi

DOI：10.1038/s41467-021-27922-0

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Abstract

En 中文

There has been recent promising experimental and theoretical evidence that quantum computational tools might enhance the precision and efficiency of physical experiments. However, a systematic treatment and comprehensive framework are missing. Here we initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms and interactive protocols. We use the QUALM framework to study two important experimental problems in quantum many-body physics: determining whether a system's Hamiltonian is time-independent or time-dependent, and determining the symmetry class of the dynamics of the system. We study abstractions of these problems and show for both cases that if the experimentalist can use her experimental samples coherently (in both space and time), a provable exponential speedup is achieved compared to the standard situation in which each experimental sample is accessed separately. Our work suggests that quantum computers can provide a new type of exponential advantage: exponential savings in resources in quantum experiments. Applying the language of computational complexity to study real-world experiments requires a rigorous framework. Here, the authors provide such a framework and establish that there can be an exponential savings in resources if an experimentalist can entangle apparatuses with experimental samples.

Keywords:

HIDDEN SUBGROUP PROBLEM

COMPLEXITY

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